NB TCN Numeracy common mistakes
NB TCN Numeracy · Understand the traps and how to avoid them.
When subtracting or dividing, the candidate drops or misplaces the digit that holds a zero (for example rewriting 4005 - 1268 as 405 - 1268 or lining digits up so the zero column is skipped), producing an answer that is off by a power of ten.
Place-value zeros carry no visible quantity, so under time pressure the candidate skips them when borrowing or aligning columns, and often writes the result without checking whether its size is plausible.
What to do instead
Before computing, write each number on a labeled place-value grid and say the value of every column aloud (thousands, hundreds, tens, ones). After computing, estimate the answer by rounding to the leading digit; if the exact result is not within about 10 percent of the estimate, recompute the zero column first.
The candidate converts a measurement in one pass using the wrong power of ten, such as treating 1 kilogram as 100 grams or 1 meter as 1000 centimeters, then applies the error consistently through the whole problem.
Metric prefixes are memorized as a list rather than as relative sizes, so the candidate recalls that a conversion factor exists but not its direction or magnitude, especially when moving between non-adjacent units.
What to do instead
Build a prefix ladder (kilo, hecto, deca, base, deci, centi, milli) once and count the number of steps moved; each step is a factor of ten. Sanity-check with a real-world anchor, such as a kilogram being about the mass of a liter of water, and reject any answer that contradicts the anchor.
The candidate computes a percentage of a number and reports it as the final answer when the question asks for the amount after an increase or decrease, or adds the percentage change to the original instead of applying it multiplicatively.
The word 'percent' triggers a single familiar procedure (multiply by the rate), and the candidate stops there without re-reading whether the question asks for the change, the new total, or the original amount.
What to do instead
Underline the question's target noun before computing, then write an explicit equation such as new = original x (1 + rate). For reverse problems, set up original x (1 + rate) = final and solve for the original rather than dividing the final by the rate alone.
When reading a table or chart, the candidate averages the category totals instead of the underlying counts, or takes the mean of already-averaged group values without weighting by group size.
Averaging feels like a single operation, so the candidate applies it to whichever numbers are visible rather than to the raw observations, and grouped data hides the differing group sizes.
What to do instead
Before averaging, write the total sum and the total count separately, weighting each group mean by its group size. State in one sentence what one observation is; if the visible numbers are not observations, reconstruct the weighted sum first.
The candidate extends a numeric or visual pattern by assuming a constant difference when the sequence is actually multiplicative or follows a second-order rule, so the next term is wrong even though the first few terms fit.
Linear change is the most practiced pattern type, and with only three or four given terms both a linear and a nonlinear rule can fit, so the candidate commits to the first rule noticed.
What to do instead
Test at least two candidate rules against every given term, computing first differences and then ratios. If neither is constant, check second differences. Write the general rule (for example term = 3n - 1) and verify it on the last given term before predicting.
The candidate confuses perimeter and area, or applies the area formula to a shape whose dimensions are given in different units without converting, so the numeric answer is dimensionally wrong.
Both quantities are computed from the same side lengths, and formulas are recalled as procedures rather than as counts of linear versus square units, so the choice is made by habit.
What to do instead
Annotate the unit of every given length and decide first whether the question asks for a distance around (linear units) or a covering (square units). Convert all lengths to one unit before substituting, and write the unit on the answer to catch mismatches.
The candidate sets up a proportion with the terms in mismatched order, pairing a quantity with the wrong category, so the cross-multiplication is arithmetically correct but solves the wrong relationship.
Proportions are often written directly from the numbers in the order they appear in the problem, without labeling which quantity each position represents.
What to do instead
Write the proportion with units attached to every term (for example dollars over items on both sides) and confirm the units cancel vertically. If the units do not align, reorder the terms before multiplying.
The candidate answers the first quantity computed rather than the quantity requested, for example giving the discount amount when the sale price was asked for, or the number of one group when a total was asked for.
Multi-step word problems reward partial progress, and the intermediate result feels like an answer, so the candidate stops once a number is produced.
What to do instead
Restate the question as a target with a unit (for example 'find the final price in dollars') before starting, and after computing, point to the line in the problem that the answer satisfies. If no line matches, continue the calculation.
The candidate rounds intermediate results aggressively and carries the rounded value forward, so a final answer that should be exact comes out slightly wrong, or the correct answer is not among the choices.
Mental arithmetic is easier with round numbers, and the candidate does not distinguish between a convenient estimate and the value that should be carried into the next step.
What to do instead
Keep full precision during intermediate steps and round only the final answer, recording the rounding rule in advance. If the answer is not among the options, redo the calculation without intermediate rounding.
The candidate misreads a scale on a graph or number line, taking each gridline as one unit when it represents five or ten, or reading a bar's height from the top of its label rather than its top edge.
Scales are read quickly from the axis labels without checking the interval between tick marks, and visual cues such as labels and gridlines compete with the actual data edge.
What to do instead
Before reading any value, compute the interval by subtracting two labeled ticks and dividing by the number of gaps between them. Read each value twice, once from the axis and once by counting gridlines from a labeled tick, and confirm the two agree.